Tuesday, March 17, 2009

Fermi's Paradox

A post at io9 got me thinking about Fermi's Paradox. The great physicist Enrico Fermi asked why, if there are numerous other technological civilizations in the universe, why have they not contacted us. You may recall in the movie Contact, an alien construct sends us a signal as soon as it picks up one of our very first television broadcasts. Why hasn't this happened?

The answer has to do with the inverse square law. The strength of a radio signal is inversely proportional to the square of the distance from its source. If they are monitoring radio signals out there, they probably still don't know we're here because by the time any radio signals from Earth reach another star, they are too weak the be distinguished from the background noise of the universe.

Remember that radio broadcasts propagate in all directions at once (stopped only by physical things like the Earth itself). So imagine a radio broadcast 1 second after it has left the Earth--it is 186K miles away. Moreover, it is occupying the surface of a sphere (we're imagining a radio signal not blocked by Earth) with a surface area of 435 billion square miles. The power of the signal hasn't degraded (let's assume), but at any spot on the sphere it is much much weaker than when it was broadcast, of course.

Now let's assume another second passes. The signal has traveled 372K miles from Earth. But now the surface area of the sphere is 1.7 trillion square miles! The signal power at any point on the sphere of propagation gets weaker in proportion to the square of its distance from its origin. So once you start getting to other stars, the signal is just lost in the background white noise of the universe. This is why it is very unlikely that civilizations communicate using radio waves or any other kind of photon, and also why movies like Contact seem fundamentally mistaken. The chance that any aliens are listening to our old TV broadcasts is very slight.

The universe may be teeming with intelligent life. But the inverse square law keeps us from communicating with photons (radio, visible light, or high-energy particles) and the limitations of the speed of light keep us from visiting one another. You might say, "Wait a second! We see photons from light years away all the time, every time we see a star." True, but that just goes to prove my point. Imagine the energy required to make a star visible for just one second. That would be roughly the energy required to make a signal visible for just one second. So let's say a civilization wants, Who-like, to broadcast its existence. It doesn't know which direction to broadcast because it doesn't know where other civilizations may be. So it has to broadcast out in all directions, i.e., it's signal will propagate along an ever-expanding sphere.

So to create a signal strong enough to be recognized, it has to basically create something with the energy of a sun. Maybe it could be done, but it would require an astonishingly advanced civilization with access to enough fuel (hydrogen or other fusionable material, I would guess) to do it. That has to be a pretty rare combination.

But a civilization that advanced (or maybe even only slightly more advanced than us) might have novel ways of communicating that don't involve sending out photons at the speed of light. Maybe they have some hitherto undiscovered (by us) quantum way of sending out a "we are here" signal. Again that leaves us out because we are technologically unable to "hear" the messages. In this scenario, one can imagine numerous interstellar conversations taking place among many civilizations--that we, in our technological ignorance, are deaf to.